Writing Linear Equations in the form y = mx + b

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0, representing where the line crosses the y-axis.

Front

How do you write a linear equation for a situation with a starting value and a constant rate of change?

Back

Use the form y = starting value + (rate of change)x.

Front

If a man is descending from 100 feet at 30 feet per minute, what is the equation for his height over time?

Back

y = 100 - 30x.

Front

What is the equation for the total cost (C) of renting a paddle boat for h hours with a $15 deposit and $2 per hour?

Back

C = 2h + 15.

Front

How do you model a situation with a startup fee and a monthly fee in slope-intercept form?

Back

Use y = monthly fee * x + startup fee.

Front

If chocolate chip cookies cost $3 each and $2 for boxing, what is the expression for the total cost?

Back

Total cost = 3x + 2, where x is the number of cookies.

Front

What is the equation for Bob's Plumbing service charge of $25 per hour plus a $40 service fee?

Back

y = 25x + 40.

Front

How do you determine the total cost of a service that has a fixed fee and a variable fee?

Back

Add the fixed fee to the product of the variable fee and the number of units.